Finite Group Databasebeta

← #14764104

Subgroups — #14764104

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622331C212yesmaximal
2C2×C4×Dic11⋊C4C211yesmaximal, characteristic
3#13069333C214yesmaximal, complemented
4#13069331C214yesmaximal, complemented
5#13068596C211yesmaximal, characteristic
6#13068594C212yesmaximal
7C11×#1797C211yesmaximal, characteristic
8C22×C42×C11C2211yescharacteristic
9C22×Dic11⋊C4C411yescharacteristic
10C22×Dic11⋊C4C411yescharacteristic
11C22×C4×Dic11C2211yescharacteristic
12C22×C4×Dic11C2211yescharacteristic
13C2×C11×C4⋊C8C2212yes—
14C2×C11×C22⋊C8C2212yes—
15C2×C11⋊#95C411yescharacteristic
16C2×C11⋊#95C411yescharacteristic
17C2×C22⋊(C11⋊C8)C2212yes—
18C2×Dic11⋊C8C2214yes—
19C2×Dic11⋊C8C2214yes—
20C2×C8×Dic11C2214yes—
21C4×Dic11⋊C4C412yes—
22C4×Dic11⋊C4C412yes—
23C4×Dic11⋊C4C2212yes—
24C4×Dic11⋊C4C2212yes—
25C2×C4⋊(C11⋊C8)C2212yes—
26#10622331—28no—
27C11×#336C2212yes—
28#10622188C2214yes—
29#10622162C2212yes—
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C23×Dic11C2×C411yescharacteristic
34C23×Dic11C2×C411yescharacteristic
35C23×Dic11C2×C411yescharacteristic
36C23×Dic11C2×C411yescharacteristic
37C22×C8×C11C2314yes—
38C2×C42×C11—42no—
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11C2×C411yescharacteristic
41C2×C42×C11C2311yescharacteristic
42C2×C42×C11C2311yescharacteristic
43C2×Dic11⋊C4—24no—
44C2×Dic11⋊C4C818yescomplemented
45C2×Dic11⋊C4C2×C412yes—
46C2×Dic11⋊C4C2×C412yes—
47C2×Dic11⋊C4C2×C412yes—
48C2×Dic11⋊C4C2×C412yes—
49C2×C4×Dic11—42no—
50C2×C4×Dic11C2×C412yes—
51C2×C4×Dic11C2×C412yes—
52C2×C4×Dic11D414yes—
53C2×C4×Dic11Q814yes—
54C2×C4×Dic11C2312yes—
55C2×C4×Dic11C2312yes—
56C22×C11⋊C8C2314yes—
57C11×C4⋊C8—42no—
58C11×C22⋊C8—24no—
59C11⋊#95C2×C412yes—
60C11⋊#95C2×C412yes—
61C11⋊#95C2×C412yes—
62C11⋊#95C2×C412yes—
63C22⋊(C11⋊C8)—24no—
64Dic11⋊C8—28no—
65Dic11⋊C8—44no—
66C8×Dic11—28no—
67C4⋊(C11⋊C8)—42no—
68#21951—111nomaximal, Sylow
69C24×C11C22×C411yescharacteristic
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11C2×C814yes—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D412yes—
84C22×C4×C11C2×Q812yes—
85C22×C4×C11C2411yescharacteristic
86C22×Dic11—22no—
87C22×Dic11—41no—
88C22×Dic11—41no—
89C22×Dic11—41no—
90C22×Dic11—41no—
91C22×Dic11—41no—
92C22×Dic11—41no—
93C22×Dic11C4⋊C414yes—
94C22×Dic11C4⋊C414yes—
95C22×Dic11C2×C814yes—
96C22×Dic11C2×C814yes—
97C22×Dic11M1614yes—
98C22×Dic11C22×C412yes—
99C22×Dic11C22×C412yes—
100C22×Dic11C22×C412yes—
101C22×Dic11C22×C412yes—
102C2×C8×C11—24no—
103C2×C8×C11—24no—
104C2×C8×C11—24no—
105C42×C11—22no—
106C42×C11—22no—
107C42×C11—41no—
108C42×C11—41no—
109Dic11⋊C4—24no—
110Dic11⋊C4—24no—
111Dic11⋊C4C2×C818yes—
112Dic11⋊C4C2×C818yes—
113C4×Dic11—24no—
114C4×Dic11—42no—
115C4×Dic11C4⋊C418yes—
116C4×Dic11C2×D414yes—
117C4×Dic11C2×Q814yes—
118C2×C11⋊C8—24no—
119C2×C11⋊C8—24no—
120C2×C11⋊C8—24no—
121C2×#431—112no—
122C2×C4×C4⋊C4—111no—
123#1939—114no—
124#1939—114no—
125#1797—111no—
126#1797—112no—
127#1797D1111yescharacteristic
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11C2×C4⋊C412yes—
133C23×C11C22×C812yes—
134C23×C11C2×M1612yes—
135C23×C11C23×C411yescharacteristic
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—44no—
151C2×C4×C11—44no—
152C2×C4×C11C2×C4⋊C412yes—
153C2×C4×C11C22×C812yes—
154C2×C4×C11C22×C812yes—
155C2×C4×C11C22×D411yescharacteristic
156C2×C4×C11C22×Q811yescharacteristic
157C2×C4×C11H(5,𝔽2)12yes—
158C2×C4×C112−1+412yes—
159C2×Dic11—22no—
160C2×Dic11—22no—
161C2×Dic11—22no—
162C2×Dic11—22no—
163C2×Dic11—22no—
164C2×Dic11—22no—
165C2×Dic11—22no—
166C2×Dic11—44no—
167C2×Dic11—44no—
168C2×Dic11—44no—
169C2×Dic11C4⋊C8116yescomplemented
170C2×Dic11C2×C4⋊C414yes—
171C2×Dic11C2×C4⋊C414yes—
172C2×Dic11C22×C814yes—
173C2×Dic11C22×C814yes—
174C2×Dic11C2×M1614yes—
175C8×C11—44no—
176C11⋊C8—44no—
177C22×C4⋊C4—111no—
178C22×C4⋊C4—111no—
179C22×C42—111no—
180C22×C42—111no—
181C22×C42C2×D1111yescharacteristic
182#431—228no—
183C2×C4⋊C8—114no—
184C2×C4⋊C8—114no—
185C2×C4⋊C8—112no—
186C2×C4⋊C8C2×D1112yes—
187C2×C22⋊C8—112no—
188C2×C22⋊C8C2×D1112yes—
189C2×C4×C8—114no—
190C4×C4⋊C4—112no—
191C4×C4⋊C4—112no—
192C4×C4⋊C4—112no—
193C4×C4⋊C4—112no—
194C2×#95—111no—
195C2×#95—111no—
196#336—114no—
197#336—112no—
198#336C2×D1112yes—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11C2×C4⋊C814yes—
206C22×C11C22×C4⋊C411yescharacteristic
207C22×C11#51811yescharacteristic
208C22×C11#51911yescharacteristic
209C22×C11C23×C811yescharacteristic
210C22×C11C22×M1611yescharacteristic
211C22×C11#56811yescharacteristic
212C22×C11#56811yescharacteristic
213C4×C11—22no—
214C4×C11—22no—
215C4×C11—22no—
216C4×C11—41no—
217C4×C11—41no—
218C4×C11#53712yes—
219C4×C11#54412yes—
220Dic11—24no—
221Dic11—24no—
222Dic11—42no—
223Dic11C2×C4⋊C818yes—
224C23×C4—111no—
225C23×C4—111no—
226C23×C4—111no—
227C23×C4—111no—
228C23×C4C4×D1111yescharacteristic
229C23×C4C4×D1111yescharacteristic
230C23×C4C22×D1111yescharacteristic
231C22×C8—114no—
232C22×C8C22×D1114yes—
233C2×C4⋊C4—118no—
234C2×C4⋊C4—112no—
235C2×C4⋊C4—112no—
236C2×C4⋊C4—112no—
237C2×C4⋊C4—112no—
238C2×C4⋊C4—224no—
239C2×C42—42no—
240C2×C42—112no—
241C2×C42—114no—
242C2×C42—114no—
243C2×C42—112no—
244C2×C42—112no—
245C2×C42—112no—
246C2×C42—442no—
247C2×C42C4×D1111yescharacteristic
248C2×C42C4×D1111yescharacteristic
249C2×C42C22×D1111yescharacteristic
250C2×C42C22×D1111yescharacteristic
251C4⋊C8—42no—
252C4⋊C8—228no—
253C4⋊C8—442no—
254C4⋊C8—444no—
255C22⋊C8—24no—
256C22⋊C8—224no—
257C4×C8—228no—
258#95—112no—
259#95—112no—
260#95—112no—
261#95—112no—
262C2×C11—24no—
263C2×C11#231611yescharacteristic
264C2×C11C22×C4⋊C811yescharacteristic
265C2×C11#290511yescharacteristic
266C2×C11#297211yescharacteristic
267C2×C11#297511yescharacteristic
268C2×C11#298211yescharacteristic
269C2×C11#298311yescharacteristic
270C24C2×C4×D1111yescharacteristic
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—114no—
279C22×C4—114no—
280C22×C4—114no—
281C22×C4—112no—
282C22×C4—112no—
283C22×C4—112no—
284C22×C4—114no—
285C22×C4—114no—
286C22×C4—112no—
287C22×C4—222no—
288C22×C4—441no—
289C22×C4—441no—
290C22×C4—441no—
291C22×C4—441no—
292C22×C4—441no—
293C22×C4—441no—
294C22×C4C8×D1114yes—
295C22×C4C2×C4×D1111yescharacteristic
296C22×C4C2×C4×D1111yescharacteristic
297C22×C4C2×C4×D1111yescharacteristic
298C22×C4C2×C4×D1111yescharacteristic
299C22×C4C2×C4×D1111yescharacteristic
300C22×C4D4×D1112yes—
301C22×C4Q8×D1112yes—
302C22×C4C23×D1111yescharacteristic
303C2×C8—24no—
304C2×C8—24no—
305C2×C8—24no—
306C2×C8—224no—
307C2×C8—224no—
308C2×C8—224no—
309C4⋊C4—118no—
310C4⋊C4—118no—
311C4⋊C4—224no—
312C4⋊C4—224no—
313C42—22no—
314C42—22no—
315C42—41no—
316C42—41no—
317C42—118no—
318C42—114no—
319C42—114no—
320C42—224no—
321C42—442no—
322C11#2195111yescharacteristic, complemented, Sylow
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23C4⋊C4×D1112yes—
328C23C2×C8×D1112yes—
329C23M16×D1112yes—
330C23C22×C4×D1111yescharacteristic
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4—114no—
348C2×C4—114no—
349C2×C4—114no—
350C2×C4—1116no—
351C2×C4—114no—
352C2×C4—114no—
353C2×C4—222no—
354C2×C4—222no—
355C2×C4—222no—
356C2×C4—222no—
357C2×C4—222no—
358C2×C4—222no—
359C2×C4—222no—
360C2×C4—444no—
361C2×C4—444no—
362C2×C4—444no—
363C2×C4C4⋊C4×D1112yes—
364C2×C4C2×C8×D1112yes—
365C2×C4C2×C8×D1112yes—
366C2×C4C2×D4×D1111yescharacteristic
367C2×C4#6703712yes—
368C2×C4C2×Q8×D1111yescharacteristic
369C2×C4#6704312yes—
370C8—44no—
371C8—444no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22D11×C4⋊C814yes—
379C22#1062301711yescharacteristic
380C22C2×C4⋊C4×D1111yescharacteristic
381C22#1062304711yescharacteristic
382C22C22×C8×D1111yescharacteristic
383C22C2×M16×D1111yescharacteristic
384C22#1062327611yescharacteristic
385C22#1062327611yescharacteristic
386C4—22no—
387C4—22no—
388C4—22no—
389C4—41no—
390C4—41no—
391C4—118no—
392C4—224no—
393C4—224no—
394C4—442no—
395C4#1062312812yes—
396C4#1062315412yes—
397C2—24no—
398C2#1307123311yescharacteristic
399C2C2×D11×C4⋊C811yescharacteristic
400C2#1307717811yescharacteristic
401C2#1307763811yescharacteristic
402C2#1307765511yescharacteristic
403C2#1307769611yescharacteristic
404C2#1307770011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C23×C8
FittingC11×#1797C2
socleC23×C11C23×C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1797D11
hypocenterC11#21951
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1797

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #13069333C2semidirect
4. #13069331C2semidirect
44. C2×Dic11⋊C4C8semidirect
169. C2×Dic11C4⋊C8semidirect
322. C11#21951semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106223312
C2×C4×Dic11⋊C42
#130693332
#130693312
#130685962
#130685942
C11×#17972
#2195111